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Let's break this down step-by-step to answer the two parts of the question.

### a. Luke's Taxable Income

1. **Income Calculation**:
   - Luke’s yearly income: $100,157
   - Dividends from shares: $340

   **Total income** = $100,157 + $340 = $100,497

2. **Deductions Calculation**:
   - Allowable deductions for car expenses: $640
   - Depreciation of photocopier: $432

   **Total deductions** = $640 + $432 = $1,072

3. **Taxable Income Calculation**:
   \[
   \text{Taxable Income} = \text{Total Income} - \text{Total Deductions}
   \]
   \[
   \text{Taxable Income} = 100,497 - 1,072 = 99,425
   \]

   **Luke's Taxable Income** is **$99,425**.

### b. Tax Payable Calculation

Luke’s taxable income falls within the range **$80,001 - $180,000**. According to the tax table, the formula for this range is:
\[
\text{Tax} = 17,547 + 0.37 \times (\text{Taxable Income} - 80,000)
\]

1. Calculate the portion above $80,000:
   \[
   \text{Excess} = 99,425 - 80,000 = 19,425
   \]

2. Calculate 37% of the excess amount:
   \[
   \text{Additional Tax} = 0.37 \times 19,425 = 7,186.25
   \]

3. Add this to the base amount for the range:
   \[
   \text{Total Tax Payable} = 17,547 + 7,186.25 = 24,733.25
   \]

### Final Answer:
- **a. Taxable Income** = $99,425
- **b. Tax Payable** = $24,733.25

Would you like more details or have any questions?

#### Related Questions:
1. How would deductions affect a higher or lower income bracket?
2. How is the marginal tax rate applied for multiple brackets in tax calculations?
3. What are some common deductions that can be subtracted from taxable income?
4. How do dividend earnings impact taxable income and total taxes?
5. If Luke’s income increased to $150,000, what would his new tax payable be?

**Tip:** Always carefully identify deductions and income additions to avoid errors in tax calculations.

Luke had a yearly income of $100,157 and earned $340 in dividends from his shares. He also had allowable deductions of $640 for car expenses and $432 in the depreciation of his photocopier. Calculate:

a. Luke’s taxable income
b. the amount of tax payable.

Learn how to calculate Luke's taxable income and tax payable based on his income, dividends, and allowable deductions. This problem covers key income tax concepts and uses tax brackets for accurate calculations. Suitable for Grades 10-12.

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